| Commit | Autor | Alter | ||
| 45edef | 1 | /************************************************************************ |
| JS | 2 | |
| 3 | POLHEMUS PROPRIETARY | |
| 4 | ||
| 5 | Polhemus | |
| 6 | P.O. Box 560 | |
| 7 | Colchester, Vermont 05446 | |
| 8 | (802) 655-3159 | |
| 9 | ||
| 10 | ||
| 11 | ||
| 12 | ||
| 13 | Copyright © 2005 by Polhemus | |
| 14 | All Rights Reserved. | |
| 15 | ||
| 16 | ||
| 17 | *************************************************************************/ | |
| 18 | ||
| 19 | // Quaternion.cpp: implementation of the CQuaternion class. | |
| 20 | // | |
| 21 | ////////////////////////////////////////////////////////////////////// | |
| 22 | ||
| 23 | #include "Quaternion.h" | |
| 24 | #include <math.h> | |
| 25 | ||
| 26 | ||
| 27 | ////////////////////////////////////////////////////////////////////// | |
| 28 | // Construction/Destruction | |
| 29 | ////////////////////////////////////////////////////////////////////// | |
| 30 | ||
| 31 | ||
| 32 | ||
| 33 | ||
| 34 | // Function name : CQuaternion::CQuaternion | |
| 35 | // Description : Default Constructor -- Orientaton 0,0,0 | |
| 36 | // Return type : | |
| 37 | CQuaternion::CQuaternion() | |
| 38 | { | |
| 39 | q0=1.0f; | |
| 40 | q1=q2=q3=0.0f; | |
| 41 | } | |
| 42 | ||
| 43 | CQuaternion::~CQuaternion() | |
| 44 | { | |
| 45 | ||
| 46 | } | |
| 47 | ||
| 48 | ||
| 49 | // Function name : CQuaternion::CQuaternion | |
| 50 | // Description : Constructs class from array of four floats | |
| 51 | // Argument : float q[] | |
| 52 | CQuaternion::CQuaternion(const float q[]) | |
| 53 | { | |
| 54 | q0=q[0]; | |
| 55 | q1=q[1]; | |
| 56 | q2=q[2]; | |
| 57 | q3=q[3]; | |
| 58 | Normalize(); | |
| 59 | ||
| 60 | } | |
| 61 | ||
| 62 | ||
| 63 | // Function name : CQuaternion::CQuaternion | |
| 64 | // Description : Constructs class from 4 individual floats | |
| 65 | // Argument : float quat0 | |
| 66 | // Argument : float quat1 | |
| 67 | // Argument : float quat2 | |
| 68 | // Argument : float quat3 | |
| 69 | CQuaternion::CQuaternion(float quat0, float quat1, float quat2, float quat3) | |
| 70 | { | |
| 71 | q0=quat0; | |
| 72 | q1=quat1; | |
| 73 | q2=quat2; | |
| 74 | q3=quat3; | |
| 75 | Normalize(); | |
| 76 | } | |
| 77 | ||
| 78 | ||
| 79 | // Function name : CQuaternion::CQuaternion | |
| 80 | // Description : Constructs class from az,el,roll in either deg or radians | |
| 81 | // Argument : float az | |
| 82 | // Argument : float el | |
| 83 | // Argument : float rl | |
| 84 | // Argument : bool deg - bool to indicate that angles are in degrees. Default is true | |
| 85 | CQuaternion::CQuaternion(float az, float el, float rl,bool deg) | |
| 86 | { | |
| 87 | float eul[3]={az,el,rl}; | |
| 88 | SetFromEulers(eul,deg); | |
| 89 | ||
| 90 | } | |
| 91 | ||
| 92 | ||
| 93 | // Function name : CQuaternion::CQuaternion | |
| 94 | // Description : Constructs class from an axis and an angle of rotation about that axis | |
| 95 | // Argument : float vect[] - 3 values representing the vector which is the axis of rotation | |
| 96 | // Argument : float angle - The angle to rotate about vect. Degrees or Radians | |
| 97 | // Argument : bool deg - bool to indicate that angles are in degrees. Default is true | |
| 98 | CQuaternion::CQuaternion(const float vect[], float angle, bool deg) | |
| 99 | { | |
| 100 | if (deg) | |
| 101 | angle*=DEG2RADS; | |
| 102 | ||
| 103 | float halfAng=angle/2.0f; | |
| 104 | ||
| 105 | q0=(float)cos(halfAng); | |
| 106 | q1=vect[0]*(float)sin(halfAng); | |
| 107 | q2=vect[1]*(float)sin(halfAng); | |
| 108 | q3=vect[2]*(float)sin(halfAng); | |
| 109 | ||
| 110 | Normalize(); | |
| 111 | } | |
| 112 | ||
| 113 | ||
| 114 | ||
| 115 | // Function name : CQuaternion::GetEuler | |
| 116 | // Description : Returns the Euler angles associated with this quaternion in deg or rads | |
| 117 | // Return type : void | |
| 118 | // Argument : float& az - azimuth returned here. | |
| 119 | // Argument : float& el - elevation returned here. | |
| 120 | // Argument : float& rl - roll returned here. | |
| 121 | // Argument : bool deg - If true returned angles are in degrees, otherwise radians. Default is true | |
| 122 | void CQuaternion::GetEuler(float& az, float& el, float& rl,bool deg) const | |
| 123 | { | |
| 124 | float mat[3][3]; | |
| 125 | float sinAz,sinEl,sinRl,cosAz,cosEl,cosRl; | |
| 126 | ||
| 127 | // create orthogonal Attitude matrix | |
| 128 | GetAttMat(mat); | |
| 129 | ||
| 130 | sinEl=-mat[2][0]; | |
| 131 | if (sinEl>1.0f) // protect from round errors causing nans | |
| 132 | sinEl=1.0f; | |
| 133 | else if (sinEl<-1.0f) | |
| 134 | sinEl=-1; | |
| 135 | ||
| 136 | cosEl=(float)sqrt(1.0f-(sinEl*sinEl)); | |
| 137 | ||
| 138 | if (fabs(cosEl)<0.001f){ | |
| 139 | sinAz=0.0f; | |
| 140 | cosAz=1.0f; | |
| 141 | } | |
| 142 | ||
| 143 | else { | |
| 144 | sinAz=mat[1][0]/cosEl; | |
| 145 | cosAz=mat[0][0]/cosEl; | |
| 146 | } | |
| 147 | ||
| 148 | sinRl=sinAz*mat[0][2]-cosAz*mat[1][2]; | |
| 149 | cosRl=-sinAz*mat[0][1]+cosAz*mat[1][1]; | |
| 150 | ||
| 151 | az=(float)atan2((double)sinAz,(double)cosAz); | |
| 152 | el=(float)atan2((double)sinEl,(double)cosEl); | |
| 153 | rl=(float)atan2((double)sinRl,(double)cosRl); | |
| 154 | ||
| 155 | if (deg){ // convert to degrees | |
| 156 | az/=DEG2RADS; | |
| 157 | el/=DEG2RADS; | |
| 158 | rl/=DEG2RADS; | |
| 159 | } | |
| 160 | ||
| 161 | } | |
| 162 | ||
| 163 | ||
| 164 | // Function name : CQuaternion::GetEuler | |
| 165 | // Description : Returns the Euler angles associated with this quaternion in deg or rads | |
| 166 | // Return type : void | |
| 167 | // Argument : float aer[] - array of 3 floats where az,el,roll are returned. | |
| 168 | // Argument : bool deg - If true returned angles are in degrees, otherwise radians. Default is true | |
| 169 | void CQuaternion::GetEuler(float aer[],bool deg) const | |
| 170 | { | |
| 171 | GetEuler(aer[0],aer[1],aer[2],deg); | |
| 172 | } | |
| 173 | ||
| 174 | ||
| 175 | // Function name : CQuaternion::Normalize | |
| 176 | // Description : normalizes the quat to a unit quaternion | |
| 177 | // Return type : void | |
| 178 | void CQuaternion::Normalize() | |
| 179 | { | |
| 180 | float mag=(float)sqrt(q0*q0+q1*q1+q2*q2+q3*q3); | |
| 181 | ||
| 182 | if (q0<0.0f) | |
| 183 | mag*=-1.0f; // make first entry pos | |
| 184 | ||
| 185 | q0/=mag; | |
| 186 | q1/=mag; | |
| 187 | q2/=mag; | |
| 188 | q3/=mag; | |
| 189 | ||
| 190 | } | |
| 191 | ||
| 192 | ||
| 193 | // Function name : CQuaternion::GetAttMat | |
| 194 | // Description : Returns the attitude matrix associated with this quaternion | |
| 195 | // Return type : void | |
| 196 | // Argument : float mat[][3] - 3x3 float array where att matrix is returned. | |
| 197 | void CQuaternion::GetAttMat(float mat[][3]) const | |
| 198 | { | |
| 199 | // create orthogonal Attitude matrix | |
| 200 | mat[0][0]=q0*q0+q1*q1-q2*q2-q3*q3; | |
| 201 | mat[0][1]=2*(q1*q2-q0*q3); | |
| 202 | mat[0][2]=2*(q1*q3+q0*q2); | |
| 203 | mat[1][0]=2*(q0*q3+q1*q2); | |
| 204 | mat[1][1]=q0*q0-q1*q1+q2*q2-q3*q3; | |
| 205 | mat[1][2]=2*(q2*q3-q0*q1); | |
| 206 | mat[2][0]=2*(q1*q3-q0*q2); | |
| 207 | mat[2][1]=2*(q0*q1+q2*q3); | |
| 208 | mat[2][2]=q0*q0-q1*q1-q2*q2+q3*q3; | |
| 209 | ||
| 210 | } | |
| 211 | ||
| 212 | ||
| 213 | ||
| 214 | ||
| 215 | ||
| 216 | ||
| 217 | // Function name : * | |
| 218 | // Description : multiplies two quaternion. | |
| 219 | // Return type : CQuaternion - The product of the multiplication. | |
| 220 | // Argument : const CQuaternion& quat2 - The quat to mult this quat by. | |
| 221 | CQuaternion CQuaternion::operator *(const CQuaternion& quat2) const | |
| 222 | { | |
| 223 | ||
| 224 | CQuaternion prod; | |
| 225 | ||
| 226 | prod.q0 = q0*quat2.q0 - q1*quat2.q1 - q2*quat2.q2 - q3*quat2.q3; | |
| 227 | prod.q1 = q0*quat2.q1 + q1*quat2.q0 + q2*quat2.q3 - q3*quat2.q2; | |
| 228 | prod.q2 = q0*quat2.q2 - q1*quat2.q3 + q2*quat2.q0 + q3*quat2.q1; | |
| 229 | prod.q3 = q0*quat2.q3 + q1*quat2.q2 - q2*quat2.q1 + q3*quat2.q0; | |
| 230 | ||
| 231 | prod.Normalize(); | |
| 232 | return prod; | |
| 233 | } | |
| 234 | ||
| 235 | // Function name : * | |
| 236 | // Description : Multiplies quaternion by a scaler | |
| 237 | // Return type : CQuaternion -- the product | |
| 238 | // Argument : const float scaler | |
| 239 | CQuaternion CQuaternion::operator *(const float scaler) const | |
| 240 | { | |
| 241 | CQuaternion prod; | |
| 242 | prod.q0=q0*scaler; | |
| 243 | prod.q1=q1*scaler; | |
| 244 | prod.q2=q2*scaler; | |
| 245 | prod.q3=q3*scaler; | |
| 246 | ||
| 247 | return prod; | |
| 248 | } | |
| 249 | ||
| 250 | ||
| 251 | ||
| 252 | // Function name : *= | |
| 253 | // Description : Multiply and assign eg. thisQuat*=thatQuat--->thisQuat=thisQuat*thatQuat | |
| 254 | // Return type : void | |
| 255 | // Argument : const CQuaternion &quat - The quat to mult this quat by. | |
| 256 | void CQuaternion::operator *=(const CQuaternion &quat) | |
| 257 | { | |
| 258 | CQuaternion prod=*this * quat; | |
| 259 | *this=prod; | |
| 260 | } | |
| 261 | ||
| 262 | ||
| 263 | // Function name : CQuaternion::GetAxisAngle | |
| 264 | // Description : Returns the axis and angle of rotation that is associated with this quaternion | |
| 265 | // Return type : void | |
| 266 | // Argument : float vect[] - array of 3 floats to receive vector representing the axis | |
| 267 | // Argument : float &angle - reference to received the angle. | |
| 268 | // Argument : bool deg - if true angle will be in degrees, otherwise radians. Default is true. | |
| 269 | void CQuaternion::GetAxisAngle(float vect[], float &angle, bool deg) const | |
| 270 | { | |
| 271 | angle=2.0f*(float)acos(q0); | |
| 272 | if (deg) | |
| 273 | angle/=DEG2RADS; | |
| 274 | ||
| 275 | float scale=(float)sqrt(q1*q1+q2*q2+q3*q3); | |
| 276 | ||
| 277 | if (fabs(scale)<0.001f){ // infinite axis, set to no rotation | |
| 278 | angle=0.0f; | |
| 279 | vect[0]=1.0f; | |
| 280 | vect[1]=vect[2]=0.0f; | |
| 281 | return; | |
| 282 | } | |
| 283 | ||
| 284 | vect[0]=q1/scale; | |
| 285 | vect[1]=q2/scale; | |
| 286 | vect[2]=q3/scale; | |
| 287 | ||
| 288 | scale=(float)sqrt(vect[0]*vect[0]+vect[1]*vect[1]+vect[2]*vect[2]); | |
| 289 | for (int i=0;i<3;i++) | |
| 290 | vect[i]/=scale; | |
| 291 | } | |
| 292 | ||
| 293 | ||
| 294 | // Function name : - | |
| 295 | // Description : Returns inverse of quaternion. eg -thisQuat --> InvthisQuat | |
| 296 | // Return type : CQuaternion - The inverse of this quaternion | |
| 297 | CQuaternion CQuaternion::operator -() const | |
| 298 | { | |
| 299 | CQuaternion inv=*this; | |
| 300 | inv.q1*=-1; | |
| 301 | inv.q2*=-1; | |
| 302 | inv.q3*=-1; | |
| 303 | return inv; | |
| 304 | } | |
| 305 | ||
| 306 | ||
| 307 | ||
| 308 | // Function name : CQuaternion::GetDeltaQuat | |
| 309 | // Description : Returns the quaternion that represents the difference between two quaternions | |
| 310 | // Return type : CQuaternion - the delta quaternion | |
| 311 | // Argument : const CQuaternion &quat - reference to a quaternion to measure the difference between | |
| 312 | CQuaternion CQuaternion::GetDeltaQuat(const CQuaternion &quat) const | |
| 313 | { | |
| 314 | /* CQuaternion inv=-(*this); | |
| 315 | return inv*quat; | |
| 316 | */ | |
| 317 | CQuaternion inv=-quat; | |
| 318 | return *this * inv; | |
| 319 | ||
| 320 | } | |
| 321 | ||
| 322 | ||
| 323 | // Function name : - | |
| 324 | // Description : Also retrieves the delta quat. eg. thisQuat-thatQuat --> GetDeltaQuat(thatQuat) | |
| 325 | // Yes this is really a multiplicaton process, but it's kind of intuitive. | |
| 326 | // Return type : CQuaternion CQuaternion::operator | |
| 327 | // Argument : const CQuaternion &quat | |
| 328 | CQuaternion CQuaternion::operator -(const CQuaternion &quat) const | |
| 329 | { | |
| 330 | return GetDeltaQuat(quat); | |
| 331 | } | |
| 332 | ||
| 333 | ||
| 334 | // Function name : CQuaternion::GetQuatVal | |
| 335 | // Description : returns the four values of the quaternion | |
| 336 | // Return type : void | |
| 337 | // Argument : float vals[] - array of 4 floats to recieve the quat values | |
| 338 | void CQuaternion::GetQuatVal(float vals[]) const | |
| 339 | { | |
| 340 | vals[0]=q0; | |
| 341 | vals[1]=q1; | |
| 342 | vals[2]=q2; | |
| 343 | vals[3]=q3; | |
| 344 | ||
| 345 | } | |
| 346 | ||
| 347 | ||
| 348 | // Function name : CQuaternion::GetQuatVal | |
| 349 | // Description : Returns an individual value of the quaternion | |
| 350 | // Return type : float - the requested value of the quaternion | |
| 351 | // Argument : int ind - the index (0-3) of the value to return. Invalid values return q0. | |
| 352 | float CQuaternion::GetQuatVal(int ind) const | |
| 353 | { | |
| 354 | float retVal; | |
| 355 | switch (ind) { | |
| 356 | case 0: | |
| 357 | default: | |
| 358 | retVal=q0; | |
| 359 | break; | |
| 360 | case 1: | |
| 361 | retVal=q1; | |
| 362 | break; | |
| 363 | case 2: | |
| 364 | retVal=q2; | |
| 365 | break; | |
| 366 | case 3: | |
| 367 | retVal=q3; | |
| 368 | } | |
| 369 | ||
| 370 | return retVal; | |
| 371 | } | |
| 372 | ||
| 373 | ||
| 374 | // Function name : CQuaternion::SetQuatVals | |
| 375 | // Description : Sets the values of the quaternion as indicated. | |
| 376 | // Return type : void | |
| 377 | // Argument : float val[] - Array of 4 floats that indicate the values to set the quaternion members to. | |
| 378 | void CQuaternion::SetQuatVals(const float val[]) | |
| 379 | { | |
| 380 | SetQuatVals(val[0],val[1],val[2],val[3]); | |
| 381 | } | |
| 382 | ||
| 383 | ||
| 384 | // Function name : CQuaternion::SetQuatVals | |
| 385 | // Description : Sets the values of the quaternion as indicated by the individual parameters | |
| 386 | // Return type : void | |
| 387 | // Argument : float w - set first quaternion value to this | |
| 388 | // Argument : float x - set second quaternion value to this | |
| 389 | // Argument : float y - set third quaternion value to this | |
| 390 | // Argument : float z - set fourth quaternion value to this | |
| 391 | void CQuaternion::SetQuatVals(const float w, const float x, const float y, const float z) | |
| 392 | { | |
| 393 | q0=w; | |
| 394 | q1=x; | |
| 395 | q2=y; | |
| 396 | q3=z; | |
| 397 | Normalize(); | |
| 398 | ||
| 399 | } | |
| 400 | ||
| 401 | bool CQuaternion::IsIdentity() | |
| 402 | { | |
| 403 | return ((q0==1.0f) && (q1==0.0f) && (q2==0.0f) && (q3==0.0f)); | |
| 404 | } | |
| 405 | ||
| 406 | void CQuaternion::Eul2Quat(float *quat, float *eul, bool isDeg) | |
| 407 | { | |
| 408 | CQuaternion q(eul[0],eul[1],eul[2],isDeg); | |
| 409 | q.MakeLargestElementPos(); | |
| 410 | q.GetQuatVal(quat); | |
| 411 | } | |
| 412 | ||
| 413 | void CQuaternion::Quats2Eul(float *eul, float *quats, bool isDeg) | |
| 414 | { | |
| 415 | CQuaternion q(quats); | |
| 416 | q.GetEuler(eul,isDeg); | |
| 417 | } | |
| 418 | ||
| 419 | void CQuaternion::MakeLargestElementPos() | |
| 420 | { | |
| 421 | float max=(float)fabs(q0); | |
| 422 | bool bChgSign=q0<0; | |
| 423 | ||
| 424 | ||
| 425 | if ((float)fabs(q1)>max){ | |
| 426 | max=(float)fabs(q1); | |
| 427 | bChgSign=q1<0; | |
| 428 | } | |
| 429 | ||
| 430 | if ((float)fabs(q2)>max){ | |
| 431 | max=(float)fabs(q2); | |
| 432 | bChgSign=q2<0; | |
| 433 | } | |
| 434 | ||
| 435 | if ((float)fabs(q3)>max){ | |
| 436 | max=(float)fabs(q3); | |
| 437 | bChgSign=q3<0; | |
| 438 | } | |
| 439 | ||
| 440 | if (bChgSign){ | |
| 441 | q0*=-1; | |
| 442 | q1*=-1; | |
| 443 | q2*=-1; | |
| 444 | q3*=-1; | |
| 445 | } | |
| 446 | } | |
| 447 | ||
| 448 | void CQuaternion::SetFromEulers(float *eul, bool deg/*=true*/) | |
| 449 | { | |
| 450 | float azHalf=eul[0]/2.0f; | |
| 451 | float elHalf=eul[1]/2.0f; | |
| 452 | float rollHalf=eul[2]/2.0f; | |
| 453 | ||
| 454 | if (deg){ | |
| 455 | azHalf*=DEG2RADS; | |
| 456 | elHalf*=DEG2RADS; | |
| 457 | rollHalf*=DEG2RADS; | |
| 458 | } | |
| 459 | ||
| 460 | q0=(float)(cos(azHalf)*cos(elHalf)*cos(rollHalf)+sin(azHalf)*sin(elHalf)*sin(rollHalf)); | |
| 461 | q1=(float)(cos(azHalf)*cos(elHalf)*sin(rollHalf)-sin(azHalf)*sin(elHalf)*cos(rollHalf)); | |
| 462 | q2=(float)(cos(azHalf)*sin(elHalf)*cos(rollHalf)+sin(azHalf)*cos(elHalf)*sin(rollHalf)); | |
| 463 | q3=(float)(sin(azHalf)*cos(elHalf)*cos(rollHalf)-cos(azHalf)*sin(elHalf)*sin(rollHalf)); | |
| 464 | ||
| 465 | ||
| 466 | Normalize(); | |
| 467 | ||
| 468 | } | |
| 469 | ||
| 470 | // Function name : CQuaternion::Slerp | |
| 471 | // Description : Spherical interpolation of quaternions. Interpolates between | |
| 472 | // this quaternion and the quaternion passed in as a parameter | |
| 473 | // Return type : CQuaternion -- The interpolated quaternion | |
| 474 | // Argument : const CQuaternion &q | |
| 475 | // Argument : float t -- value between 0 and 1 which indicates the distance between | |
| 476 | // quaternions to interpolate | |
| 477 | CQuaternion CQuaternion::Slerp(const CQuaternion &q, float t) const | |
| 478 | { | |
| 479 | ||
| 480 | // qa*sin((1-t)theta)+qb*sin(t*theta) | |
| 481 | // q= ---------------------------------- | |
| 482 | // sin(theta) | |
| 483 | ||
| 484 | // 2*theta = qa.q0*qb.q0+qa.q1*qb.q1+qa.q2*qb.q2+qa.q3*qb.q3 | |
| 485 | ||
| 486 | ||
| 487 | ||
| 488 | ||
| 489 | float angle; | |
| 490 | ||
| 491 | if (t>=1.0f) | |
| 492 | return CQuaternion(q); | |
| 493 | ||
| 494 | if (t<=0.0f) | |
| 495 | return CQuaternion(*this); | |
| 496 | ||
| 497 | ||
| 498 | float dot=q0*q.q0+q1*q.q1+q2*q.q2+q3*q.q3; | |
| 499 | angle=(float)(acos(dot))/2.0f; | |
| 500 | if (angle<0.0f) | |
| 501 | angle*=-1; | |
| 502 | ||
| 503 | float coeff1,coeff2; | |
| 504 | ||
| 505 | if (angle==0.0f){ | |
| 506 | coeff1=1-t; | |
| 507 | coeff2=t; | |
| 508 | } | |
| 509 | else { | |
| 510 | ||
| 511 | coeff1=(float)sin((1.0f-t)*angle)/(float)sin(angle); | |
| 512 | coeff2=(float)sin(t*angle)/(float)sin(angle); | |
| 513 | } | |
| 514 | ||
| 515 | CQuaternion res=*this*coeff1+q*coeff2; | |
| 516 | res.Normalize(); | |
| 517 | ||
| 518 | return res; | |
| 519 | } | |
| 520 | ||
| 521 | // Function name : + | |
| 522 | // Description : Adds to quaternions | |
| 523 | // Return type : CQuaternion -- the sum | |
| 524 | // Argument : const CQuaternion &q1 | |
| 525 | // Argument : const CQuaternion &q2 | |
| 526 | CQuaternion CQuaternion::operator +(const CQuaternion &q) const | |
| 527 | { | |
| 528 | CQuaternion sum; | |
| 529 | sum.q0=q0+q.q0; | |
| 530 | sum.q1=q1+q.q1; | |
| 531 | sum.q2=q2+q.q2; | |
| 532 | sum.q3=q3+q.q3; | |
| 533 | ||
| 534 | return sum; | |
| 535 | ||
| 536 | } | |
| 537 | ||
| 538 | ||
| 539 | ||
| 540 | ||
| 541 | void CQuaternion::GetAngle(float &a,bool deg) | |
| 542 | { | |
| 543 | a=2.0f*(float)acos(q0); | |
| 544 | if (deg) | |
| 545 | a/=DEG2RADS; | |
| 546 | ||
| 547 | } | |
